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Variational Methods for Discontinuous Structures

International Workshop at Villa Erba (Cernobbio), Italy, July 2001

  • Conference proceedings
  • © 2002

Overview

Editors:
  1. Gianni Maso

    1. Scuola Internazionale Superiore di Studi, Avanzati (SISSA), Trieste, Italy

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  2. Franco Tomarelli

    1. Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, Milano, Italy

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 51)

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Table of contents (12 papers)

  1. Front Matter

    Pages i-x
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  2. A Model for Mixtures of Micromagnetic Materials allowing Existence and Regularity

    • Emilio Acerbi
    Pages 1-8

  3. Variational Properties of a Model for Image Segmentation with Overlapping Regions

    • Giovanni Bellettini, Riccardo March
    Pages 9-17

  4. Variational Theory of Weak Geometric Structures: The Measure Method and Its Applications

    • Guy Bouchitté, Ilaria Fragalà
    Pages 19-40

  5. Optimal Transportation Problems with Free Dirichlet Regions

    • Giusppe Buttazzo, Edouard Oudet, Eugene Stepanov
    Pages 41-65

  6. Local Minimizers for a Free Gradient Discontinuity Problem in Image Segmentation

    • Michele Carriero, Antonio Leaci, Franco Tomarelli
    Pages 67-80

  7. Irrigation

    • Vicent Caselles, Jean-Michel Morel
    Pages 81-90

  8. Symmetrization and Functionals Defined on BV

    • Andrea Cianchi, Nicola Fusco
    Pages 91-102

  9. Interface Energies and Structured Deformations in Plasticity

    • Gianpietro Del Piero
    Pages 103-116

  10. Higher Order Variational Problems and Phase Transitions in Nonlinear Elasticity

    • Irene Fonseca, Giovanni Leoni
    Pages 117-140

  11. Unstable Crystalline Wulff Shapes in 3D

    • Maurizio Paolini, Franco Pasquarelli
    Pages 141-153

  12. Dimension Reduction in Continuum Mechanics

    • Danilo Percivale
    Pages 155-170

  13. Reaction-Diffusion Equations and Learning

    • Jayant Shah
    Pages 171-182

  14. Back Matter

    Pages 183-188
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Keywords

About this book

This volume contains the Proceedings of the International Workshop Variational Methods For Discontinuous Structures, which was jointly organized by the Dipar­ timento di Matematica Francesco Brioschi of Milano Politecnico and the Interna­ tional School for Advanced Studies (SISSA) of Trieste. The Conference took place at Villa Erba Antica (Cernobbio) on the Lago di Como on July 4- 6, 2001. In past years the calculus of variations faced mainly the study of continuous structures, say particularly problems with smooth solutions. One of the deepest and more delicate problems was the regularity of weak solutions. More recently, new sophisticated tools have been introduced in order to study discontinuities: in many variational problems solutions develop singularities, and sometimes the most interesting part of a solution is the singularity itself. The conference intended to focus on recent developments in this direction. Some of the talks were devoted to differential or variational modelling of image segmentation, occlusion and textures synthesizing in image analysis, varia­ tional description of micro-magnetic materials, dimension reduction and structured deformations in elasticity and plasticity, phase transitions, irrigation and drainage, evolution of crystalline shapes; in most cases theoretical and numerical analysis of these models were provided. viii Preface Other talks were dedicated to specific problems of the calculus of variations: variational theory of weak or lower-dimensional structures, optimal transport prob­ lems with free Dirichlet regions, higher order variational problems, symmetrization in the BV framework.

Editors and Affiliations

  • Scuola Internazionale Superiore di Studi, Avanzati (SISSA), Trieste, Italy

    Gianni Maso

  • Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, Milano, Italy

    Franco Tomarelli

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